Real-Time Anomaly Detection And Correlation Of Time-Series Data

ABSTRACT

The present disclosure provides systems and methods for detecting and correlating anomalous time-series data. A system may receive and process time-series data associated with one or more network data streams to generate sets of aligned time-series data. The system may detect anomalous time-stamped data points in the sets of aligned time series data and generate groups of annotated time-series data. The annotation identifies specific time-stamped data points as anomalous. The system may determine the number of anomalous groups of annotated time-series data within all groups of annotated time-series data and may further determine the probability that one or more anomalous groups belong to at least one of the groups of annotated time-series data using a generative statistical model and outputting one or more correlated anomalous groups. The system may generate a detailed statistical report for each correlated anomalous group and output an aggregated statistical report for the correlated groups.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 15/816,483, filed Nov. 17, 2017, the disclosure of which isincorporated herein by reference.

BACKGROUND

A time series is a series of data points indexed in time order. A widevariety of data can be represented as a time series, such as dailytemperatures, closing values of financial markets, as well as datarelating to network performance such as latency, packet loss or networkoutages. Time series data can include one or more data points that maybe anomalous or otherwise outside the normally expected range of valuesthat is commonly associated with the specific variable being representedin the time series. To better understand the nature of the anomaloustime series data points, it is advantageous to detect and accuratelyclassify the anomalous data from the expected, non-anomalous datapresent in the time series.

Network data can often be represented as a time series. For example,many network performance characteristics can be measured as a functionof time such as packet or link latency or the amount of up-time ordown-time exhibited by a particular network entity, such as a switch, orby a collection of network entities. Evaluating network time series datafor anomaly detection and correlation can rapidly become a complexproblem as the overall network size and the dynamic interconnectednessof participating network entities constantly changes. For example, asphysical networks become larger with a greater number ofinterconnections, the likelihood of network outages or failure eventsmay also rise. In many cases, the network failures may be correlated,for example certain sets of links may tend to fail simultaneously due tosingle points of failures within the network. Similarly, latenciesbetween large groups of endpoints pairs could increase simultaneouslydue to the degradation of shared portions of their path(s). Evaluatingstreams of network data in real-time to identify network failure eventswould greatly benefit network efficiency and operation, however doing socan be difficult because the network data often includes noise, missingvalues, and/or inconsistent time granularity. In addition, real-timemonitoring and evaluation involves processing extremely large amounts ofnetwork data, which can be difficult to scale as the size and complexityof modern network infrastructures grow.

SUMMARY

According to one aspect, the disclosure relates to acomputer-implemented method for detecting and correlating anomaloustime-series data. The method includes receiving a plurality oftime-series data associated with one or more network data streams. Themethod also includes processing the received plurality of time-seriesdata and generating one or more sets of aligned time-series data. Themethod includes detecting anomalous time-stamped data points in each ofthe one or more sets of aligned time-series data and generating one ormore groups of annotated time-series data. The annotation identifies oneor more specific time-stamped data points as anomalous. The method alsoincludes determining the number of anomalous groups of annotatedtime-series data within all of the one or more groups of annotatedtime-series data. The method includes determining the probability thatone or more anomalous groups of annotated time-series data belong to atleast one of the groups of annotated time-series data using a generativestatistical model and outputting one or more correlated anomalousgroups. The one or more anomalous groups are determined to be correlatedbased on the anomalous groups including one or more statisticallycorrelated anomalous time-stamped data points. The method also includesprocessing each of the one or more outputted correlated anomalous groupsto generate a detailed statistical report for each correlated anomalousgroup. The method also includes outputting an aggregated statisticalreport for the one or more correlated anomalous groups.

In some implementations, the received time-series data includes one ormore of binary data types, categorical data types, or real-valued datatypes. In some implementations, the one or more network data streams arereceived from external sources. In some implementations, processing thereceived plurality of time-series data includes one or more ofnormalizing the time-series data, inputting missing values, performingtime-stamp up-sampling, performing time-stamp down-sampling, andremoving noise from the received plurality of time-series data. In someimplementations, the steps of processing the received plurality oftime-series data are performed in parallel. In some implementations, thegenerated one or more sets of aligned time-series data are temporallyaligned. In some implementations, detecting anomalous time-stamped datapoints in each of the one or more sets of aligned time-series data isperformed using one or more virtual interfaces. The one or more virtualinterfaces are determined based on the data type of the alignedtime-series data. In some implementations, the one or more of virtualinterfaces may detect anomalous time-stamped data points in parallel. Insome implementations, determining the number of anomalous groups withinall of the one or more annotated sets of time-series data is performedusing a locality sensitive hashing algorithm. In some implementations,the generative statistical model is a Latent Dirichlet Allocation model.In some implementations, determining the probability that one or moreanomalous group of annotated time-series data belong to at least one ofthe groups of annotated time-series data and outputting one or morecorrelated anomalous groups is performed in parallel. In someimplementations, the one or more anomalous groups are determined to benot correlated based on the one or more anomalous groups not includingone or more statistically correlated anomalous time-stamped data points.In some implementations, the detailed statistical report for eachcorrelated anomalous group identifies the Pearson correlationcoefficients, Jaccard similarities, and/or Bayes factors of eachcorrelated anomalous group. In some implementations, the aggregatedstatistical report is output to users via one or more applicationprogramming interfaces. In some implementations, the aggregatedstatistical report is human-interpretable. In some implementations, theaggregated statistical report includes the probabilities of singlenetwork entity failures and grouped network entity failures.

According to certain aspects of the present disclosure, a system fordetecting and correlating anomalous time-series data is provided. Thesystem includes a memory storing computer-readable instructions and oneor more generative statistical models. The system also includes aprocessor configured to execute the computer-readable instructions. Theinstructions, when executed cause the processor to receive a pluralityof time-series data associated with one or more network data streams.The processors are further configured to process the received pluralityof time-series data and generate one or more sets of aligned time-seriesdata. The processors are further configured to detect anomaloustime-stamped data points in each of the one or more sets of alignedtime-series data and generate one or more groups of annotatedtime-series data. The annotation identifies one or more specifictime-stamped data points as anomalous. The processors are furtherconfigured to determine the number of anomalous groups of annotatedtime-series data within all of the one or more groups of annotatedtime-series data. The processors are further configured to determine theprobability that one or more anomalous groups of annotated time-seriesdata belong to at least one of the groups of annotated time-series datausing a generative statistical model and output one or more correlatedanomalous groups. The one or more anomalous groups are determined to becorrelated based on the anomalous groups including one or morestatistically correlated anomalous time-stamped data points. Theprocessors are further configured to process each of the one or moreoutputted correlated anomalous groups to generate a detailed statisticalreport for each correlated anomalous group. The processors are furtherconfigured to output an aggregated statistical report for the one ormore correlated anomalous groups.

In some implementations, the processors are configured to receivetime-series data including one or more of binary data types, categoricaldata types, or real-valued data types. In some implementations, theprocessors are configured to receive one or more network data streamsfrom external sources. In some implementations, the processors areconfigured to process the received plurality of time-series data by oneor more of normalizing the time-series data, inputting missing values,performing time-stamp up-sampling, performing time-stamp down-sampling,and removing noise from the received plurality of time-series data. Insome implementations, the processors are configured to perform the stepsof processing the received plurality of time-series data in parallel. Insome implementations, the processors are configured to generate one ormore sets of aligned time-series data that are temporally aligned. Insome implementations, the processors are configured to perform detectinganomalous time-stamped data points in each of the one or more sets ofaligned time-series data using one or more virtual interfaces. The oneor more virtual interfaces are determined based on the data type of thealigned time-series data. In some implementations, the processors areconfigured with one or more virtual interfaces to detect anomaloustime-stamped data points in parallel. In some implementations, theprocessors are configured to determine the number of anomalous groupswithin all of the one or more annotated sets of time-series data using alocality sensitive hashing algorithm. In some implementations, thegenerative statistical model is a Latent Dirichlet Allocation model. Insome implementations, the processors are configured to determine theprobability that one or more anomalous groups of annotated time-seriesdata belong to at least one of the groups of annotated time-series dataand output one or more correlated anomalous groups parallel. In someimplementations, the processors are configured to determine that one ormore anomalous groups are not correlated based on the one or moreanomalous groups not including one or more statistically correlatedanomalous time-stamped data points. In some implementations, theprocessors are configured to identify in the detailed statistical reportfor each correlated anomalous group the Pearson correlationcoefficients, Jaccard similarities, and/or Bayes factors of eachcorrelated anomalous group. In some implementations, the processors areconfigured to output the aggregated statistical report to users via oneor more application programming interfaces. In some implementations, theaggregated statistical report is human-interpretable. In someimplementations, aggregated statistical report includes theprobabilities of single network entity failures and grouped networkentity failures.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide furtherunderstanding and are incorporated in and constitute a part of thisspecification, illustrate disclosed embodiments and together with thedescription serve to explain the principles of the disclosedembodiments. In the drawings:

FIG. 1 illustrates an example functional block diagram of a system fordetecting and correlating anomalous time-series data.

FIG. 2 illustrates an example architecture for detecting and correlatinganomalous time-series data in a distributed server architecture.

FIG. 3 is a flowchart showing an example method for detecting andcorrelating anomalous time-series data.

FIG. 4 is a flowchart showing an example method for generating alignedtime-series data.

FIG. 5 is a flowchart showing an example method for generating annotatedtime-series data.

FIG. 6 is a flowchart showing an example method for correlatinganomalous groups of time-series data.

FIG. 7 illustrates an example functional block diagram for generatingdetailed statistical reports for each correlated anomalous group and foroutputting an aggregated statistical report.

FIG. 8 is a block diagram of an example computing system.

In one or more implementations, not all of the depicted components ineach figure may be required, and one or more implementations may includeadditional components not shown in a figure. Variations in thearrangement and type of the components may be made without departingfrom the scope of the subject disclosure. Additional components,different components, or fewer components may be utilized within thescope of the subject disclosure.

DETAILED DESCRIPTION

The disclosed system includes a number of components to collect andprocess network data streams. The system components can process thenetwork data streams in real-time by performing the disclosed method ofdetecting and correlating anomalies from the collected network datastreams. The system includes a data collection component to receive thenetwork data streams from external data sources and perform datacleaning. For example, the data collection component may be a module tonormalize data stream values, input missing values, perform timestampup-sampling or down-sampling, as well as removing noise from the datastream values. The data collection component may perform the datacleaning steps in parallel. The data collection component outputs thecleaned data as set or groups of aligned time series data.

The aligned time series data can further be processed by an anomalydetection component. The anomaly detection component may include aplurality of virtual interfaces that are configured to perform anomalydetection based on the various data types that are present in thealigned time series data that are associated with the collected networkdata streams. For example, latency data received in histogram format maybe converted to cumulative distribution function curves that are thennormalized before calculating the difference in the area under thecurve. In addition, the virtual interface may support processing networkoutage data as binary variables, as well as processing data whichincludes real-values, such as conditions where a data spike may indicatean anomaly. In some implementations, the anomaly detection component mayperform the processing for various data types in parallel. The anomalydetection component may annotate specific time-stamped data pointswithin the time-series data determined to be anomalous and may outputgroups or sets of annotated time series data.

The sets of annotated (anomalous) time series data are received by aglobal correlation component and processed by dividing the groups ofannotated (anomalous) time series data into smaller groups to avoidcross-group correlation. The groups may then be further processed inparallel. A locality sensitive hashing function or algorithm is used todetermine the number of anomalous groups within or across all of thesets of annotated time series data. The number of groups is thenprovided as an input to a generative statistical model, such as a LatentDirichlet Allocation (LDA) model, to find the probability that one ormore groups of annotated time series data belong to one of the groups ofannotated time series data determined by the locality sensitive hashingfunction. The method steps performed by the global correlation componentmay also be performed in parallel. The output of the global correlationcomponent is a grouping of the time series data such that the anomalieswithin a group are statistically correlated and the anomalies acrossgroups are not statistically correlated. Using LDA, network entitygroupings may be determined based on temporal failure patterns withoutrequiring exhaustive pairwise time series data comparison.

Multiple local correlation components process the groups of anomaloustime series data generated by the global correlation component inparallel and output statistics for a particular group of anomalous timeseries data. For example, one local correlation component may outputstatistical data for a particular group of anomalous time series dataincluding, but not limited to, Pearson correlation coefficients, Jaccardsimilarities, and/or Bayes factors.

A reporting component aggregates the statistics generated by the localcorrelation components and presents the data as reports to users viavarious application programming interfaces (APIs). The reports and dataincluded therein are human-interpretable and provide, for a givenanomaly group, the probabilities of single and grouped network entityfailures which can used for network planning and data-drivenoptimization of network resources.

The system and method disclosed herein addresses the problem ofautomatically detecting and correlating anomalous events from largeamounts of time-series data in real-time or near real-time. Advances incomputer processing, internet technologies, sensor architectures, andcommunication networking have created an unprecedented data ecospherethat is available for analysis using similarly advanced techniques indata science such as data mining, artificial intelligence, machinelearning, classification and visualization. Gaining insight from suchlarge volumes of data can be time-consuming, error prone, and is oftenlimited by the configuration of specific tools or resources. Oneapproach to help manage the task of evaluating such large volumes ofdata is to evaluate outliers or anomalous data points that are presentin the volumes of data. While outliers tend to be ignored as minor,unexplainable inconsistencies associated with the data being collected,outliers can also shed important insight into the root cause of theanomalous data. This is especially true in network data, where anomaloustime-series data may indicate the failure of a particular networkdevice, network interface or connection between networks or networkdevices. As the complexity and size of modern sensor and communicationnetworks increase, the inter-connectedness of network elements alsoincreases which means larger volumes of time-series data must beevaluated in order to accurately assess anomalous data points so thatthe root cause of the anomaly can be better understood. Traditionalmethods to detect and evaluate network time-series data anomalies, suchas rule- or threshold-based alerting, dashboard inspection, or periodicspot checking of data, are not suitable given the enormous amounts ofdata being generated in modern networks and are also not robust tohandle noisy, fluctuating anomaly data. In addition, traditionallynetwork failure data has been represented as binary data values. Forexample, a binary value for a particular network failure may beassociated with each network link. If the link is operational, the valuewould be “0”, if the link has failed, the value would be “1”, or viceversa. Using only binary values for anomaly detection limits thecorrelative inferencing such that latent factors, which are associatedwith network failure events, remain un-discovered and hidden providingreduced insight into the root cause of a particular network failure. Aswill be discussed in more detail below, using real-valued data streams,such as latency or packet loss, instead of solely binary data canimprove the ability to robustly correlate latent or hidden factors (ornetwork entities) that are likely to behave anomalously.

Solutions to these problems may be achieved by the disclosed systems andmethods whereby network data streams, and corresponding time-series datawithin the network data streams, may be monitored and evaluated in anautomated, near real-time manner to detect anomalous network failureevents in order to condense or correlate the failure events into groupsof outliers so that the root causes of the failures can be determined.This solution can also help improve network planning by identifyingcritical failure modes and modeling the failure modes accurately suchthat future occurrences can be more easily associated with a previouslydetermined root cause. In addition, the disclosed systems and methodsenable anomaly detection and correlation to be performed in a way thatmay afford greater scalability and parallelization compared totraditional techniques because the components of the system may beconfigured in a distributed architecture as will be described inrelation to FIG. 2. The distributed architecture enables greaterparallel processing of the large volumes of network failure data thatmay be generated by larger, more complex networks. The system and methodmay also provide more robust processing of noisy, uncorrelated anomalydata by removing or ignoring small individual fluctuations in the datathat may distort anomaly correlation. In addition, the system and methodare not limited to detecting and correlating network failure anomaliesbased solely on binary failure data. The system and method function toprocess real-valued network failure data types in order to more robustlydetect and correlate anomalies that may be associated with latent orhidden factors (or network entities).

FIG. 1 illustrates an example functional block diagram of a system 100for detecting and correlating anomalous time-series data. The system 100includes a plurality of time-series data sources, shown as binarytime-series data source 105 a, categorical time-series data source 105b, and real-value time-series data source 105 c. The plurality oftime-series data sources will each generally be referred to as atime-series data source 105 or collectively as time-series data sources105. The system 100 also includes an anomaly detection and correlationsystem 110. The anomaly detection and correlation system 110 includes adata collector 130 and an anomaly detection sub-system 135. The anomalydetection sub-system 135 includes a plurality of detectors 140, such asdetector 140 a, 140 b, and 140 c. The plurality of detectors 140 willeach generally be referred to as detector 140 or collectively asdetectors 140. The anomaly detection and correlation system 110 alsoincludes an anomaly correlation sub-system 145. The anomaly correlationsub-system 145 includes a global correlator 150 and a plurality of localcorrelators 155, such as local correlators 155 a, 155 b, and 155 c. Theplurality of local correlators will each generally be referred to aslocal correlator 155 or collectively as local correlators 155. Theanomaly detection and correlation system 110 also includes a reportingmodule 160.

As shown in FIG. 1, the system 100 includes a plurality of time-seriesdata sources 105 that store network time-series data. The time-seriesdata sources 105 are sources of time-series data. The time-series datastored in the time-series data sources 105 is received by the datacollector 130 of the anomaly detection and correlation system 110. Thetime-series data sources 105 may store time-series data that may beassociated with one or more aspects of a network's performance over aperiod of time, such as latency values, link status (e.g., the link isfunctional or non-functional), and/or network entity ownership.

The time-series data stored in the data sources 105 may include avariety of time-series data types. For example, as shown in FIG. 1, thebinary time-series data source 105 a may store binary time-series data.Binary time-series data may include data, measured as a function oftime, that represents one of only two possible values. In this example,binary time-series data source 105 a may store binary time-series datasuch as link connectivity status as measured over time, where thetime-series value of the link connectivity status may be only one of twovalues (e.g., functional (1) or non-functional (0)) or vice versa. Asfurther shown in FIG. 1, the time-series data sources 105 may alsoinclude a categorical time-series data source 105 b. The categoricaltime-series data source 105 b may store categorical time-series datatypes. Categorical time-series data types may include data, measured asa function of time, which represents one of multiple possible values (orcategories). For example, a categorical time-series data source 105 bmay store categorical time-series data such as the network operatorassociated with a particular network entity, such as a switch or routerthat is deployed in a network. In this example, the categoricaltime-series data may represent the name of the network operatorassociated with a specific network entity. The network operator may be asingle operator identified from multiple possible operators. As furthershown in FIG. 1, the time-series data sources 105 may also include areal-value time-series data source 105 c. The real-value time-seriesdata source 105 c may store real-value time-series data. Real-valuetime-series data may include data, measured as a function of time, whichrepresents numerical or real-value data. For example, a real-valuedata-source 105 c may store real-value time-series data such as latencyvalues that are associated with a particular link or network device in apacket-switched network, measured in milliseconds. In this example, thereal-value time-series data may include a specific numerical value thathas been measured as a function of time.

In some implementations, the time-series data sources 105 may storetime-series data that is associated with one or more network datastreams. The network data streams may be received from external sources.For example, the network data streams may be associated with networksthat are located remotely from the time-series data sources 105 or theanomaly detection and correlation system 110.

As further shown in FIG. 1, the system 100 includes an anomaly detectionand correlation system 110. The anomaly detection and correlation system110 includes multiple components that are configured to detect andcorrelate anomalies in time-series data that is associated with one ormore network data streams and received from the time-series data sources105.

As shown in FIG. 1, the anomaly detection and correlation system 110includes a data collector 130. The data collector 130 receives thetime-series data from the time-series data sources 105 and prepares thedata for anomaly detection and correlation processing. In broad terms,the data collector 130 applies a variety of data cleaning methods on thereceived time-series data in order to prepare the data for efficientdetection and correlation processing. For example, the data collectormay perform methods on the received time-series data including, but notlimited to, normalization, missing value imputation, timestamp up- ordown-sampling, as well as noise removal. In addition, the data collector130 aligns the time-series data temporally and generates one or moresets of temporally aligned time-series data. In some implementations,the data collector 130 may fetch the time-series data from thetime-series data sources 105 to perform the data cleaning methods.Additional details of the data cleaning methods that are performed bythe data collector 130 will be described in more detail in relation toFIG. 4.

As further shown in FIG. 1, the anomaly detection and correlation system110 includes an anomaly detection sub-system 135. The anomaly detectionsub-system 135 receives the temporally aligned time-series data that wasgenerated by the data collector 130 and performs anomaly detection onthe aligned time-series data. The anomaly detection sub-system 135includes a plurality of detectors such as detectors 140. The detectors140 may be virtual interfaces for anomaly detection whose implementationcorresponds to a particular time-series data type. The detectors 140apply different anomaly detection techniques based on the time-seriesdata type of the aligned time-series data received from the datacollector 130 and annotate the anomalous time-stamped data points thatwere detected. The anomaly detection sub-system 135 generates groups ofannotated (anomalous) time-series data for output. Additional details ofthe anomaly detection methods that are performed by the anomalydetection sub-system 135 will be described below in more detail inrelation to FIG. 5.

As shown in FIG. 1, the anomaly detection and correlation server 110includes an anomaly correlation sub-system 145. The anomaly correlationmodule 145 receives as input the groups of annotated time-series dataand performs correlation techniques on the data to output a grouping oftime-series data such that the anomalies within each group arestatistically correlated to each other and the anomalies acrossdifferent groups are not correlated or are substantially less correlatedto each other. The anomaly correlation sub-system 145 includes a globalcorrelator 150. The global correlator 150 divides the inputted groups ofannotated time-series data into smaller groups so there is little or nocross-correlation between groups. The global correlator 150 performscorrelation on the groups using a combination of hashing techniques todetermine the number of anomalous groups or number of potentiallyanomalous groups across all inputted groups of annotated time-seriesdata and subsequently provides the groups as inputs to a generativestatistical model, such as a Latent Dirichlet Allocation model in orderto determine the probability of each time-series belonging to only onegroup of the inputted groups of annotated time-series data. The outputof the generative statistical model is a distribution of networkentities that are associated with groups of correlated anomaloustime-series data. In this way, heavier-weighted network entities, e.g.,those with higher correlative probabilities, are most likely to failsimultaneously over the time period associated with the timestamped dataof the inputted groups of annotated time-series data. In this way groupsof network entities can be discovered as the root causes of anomaloustime-series data based on the temporal failure patterns of thetime-series data without requiring exhaustive pairwise comparisons ofthe time-series data.

As further shown in FIG. 1, the anomaly correlation sub-system 145includes a plurality of local correlators, such as local correlators 155a-155 c. The plurality of local collectors will be generally referred toas local correlators 155. The local correlators 155 each receive arespective group of correlated anomalous time-series data output by theglobal correlator 150. The local correlators 155 may perform additionalstatistical processing on each of the groups of correlated anomaloustime-series data. The statistical processing performed by the localcorrelators 155 on the groups of correlated anomalous time-series dataand the detected anomalies therein may include, but are not limited to,determining the Pearson correlation coefficient, the Jaccardsimilarities, and/or the Bayes factors. The local correlators 155 mayoutput a detailed statistical report for each group of correlatedanomalous time-series data which includes the results of the statisticalprocessing performed by the local correlators 155. Additional details ofthe global correlator 150 and the local correlator's 155 functionalitywill be described below in relation to FIGS. 6 and 7, respectively.

In some implementations, a feedback loop may exist between the anomalycorrelation sub-system 145 and the anomaly detection sub-system 135 asshown in FIG. 1 with the bi-directional arrow connecting the twosub-systems. In this way, the detectors 140 may be trained using thecorrelation results generated by the global correlator 150. Thisfeedback loop may enable the detectors 140 to detect anomalies withgreater accuracy.

As shown in FIG. 1, the anomaly detection and correlation systemincludes a reporting module, such are reporting module 160. Thereporting module 160 may aggregate the detailed statistical reports thatwere output from the local correlators 155 and may generate anaggregated statistical report for the groups of correlated anomaloustime-series data. The aggregated statistical reports may be madeavailable to users through one or more application programminginterfaces (APIs). Additional details of the reporting module 160functionality will be described below in relation to FIG. 7.

The system 100 shown in FIG. 1 includes an anomaly detection andcorrelation system 110 including a plurality of components (or modules)and subsystems. Each sub-system may further include one or morecomponents (or modules). As shown in FIG. 1, the plurality of components(or modules) and subsystems in the anomaly detection and correlationsystem 110 are configured on a single server and may operate in parallelon the single server. As will be shown in FIG. 2, the plurality ofcomponents (or modules) and subsystems in the anomaly detection andcorrelation system 110 may also be configured in an arrangementincluding distributed servers in order to increase the parallelprocessing of time-series data for anomaly detection and correlation.

FIG. 2 illustrates an example distributed server architecture fordetecting and correlating anomalous time-series data. The architecture200 includes identical components as described in relation to FIG. 1,however, the plurality of components and subsystems shown in FIG. 2 arearranged in a configuration of distributed servers that are connectedvia a network, instead of arranged within a single server as shown inFIG. 1. The functionality of the individual components and sub-systemsshown in FIG. 2 is identical to the functionality of the individualcomponents and sub-systems shown in FIG. 1.

The architecture 200 shown in FIG. 2 includes time-series data sources105, an anomaly detection system 205, a network 210, a globalcorrelation sub-system 215, and a plurality of local correlationsub-systems 220 a-220 c. The plurality of local correlation sub-systems220 a-c will be collectively referred to as local correlationsub-systems 220. The architecture 200 also includes a reportingsub-system 225.

As shown in FIG. 2, a plurality of time-series data sources, such astime-series data sources 105 described in relation to FIG. 1, arecommunicatively coupled to a network, such as the network 210. Thetime-series data sources 105 store time-series data of different datatypes that may be processed for anomaly detection and correlation. Thestored time-series data may be transmitted over a network and receivedby the anomaly detection system 205. The anomaly detection system 205includes a data collector, such as the data collector 130 described inrelation to FIG. 1, and an anomaly detection sub-system, such as theanomaly detection sub-system 135 described in relation to FIG. 1. Theanomaly detection sub-system 135 includes a plurality of detectors 140a-140 c, which will each generally be referred to as detector 140 orcollectively as detectors 140. The anomaly detection system 205 receivestime-series data from the time-series data sources 205 over network 210for processing by the data collector 130 and subsequently by thedetectors 140 that are configured in the anomaly detection sub-system135.

As further shown in FIG. 2, the architecture 200 includes a network 210.The network 210 can include, for example, any one or more of a personalarea network (PAN), a local area network (LAN), a campus area network(CAN), a metropolitan area network (MAN), a wide area network (WAN), abroadband network (BBN), the Internet, and the like. Further, thenetwork can include, but is not limited to, any one or more of thefollowing network topologies, including a bus network, a star network, aring network, a mesh network, a star-bus network, tree or hierarchicalnetwork, and the like. The network 210 enables the communication of datato be processed by the distributed servers configured to detect andcorrelate anomalous time-series data.

As shown in FIG. 2, the architecture 200 includes a global correlationsub-system 215. The global correlation sub-system 215 includes a globalcorrelator, such as the global correlator 150 described in relation toFIG. 1. The global correlation sub-system 215 receives annotatedtime-series data over the network 210 from the anomaly detection system205.

As further shown in FIG. 2, the architecture 200 includes a plurality oflocal correlation sub-systems 220 a-220 c. The plurality of localcorrelation sub-systems will each generally be referred to as localcorrelation sub-system 220 or collectively referred to as localcorrelation sub-systems 220. Each respective local correlation subsystem220 includes a local correlator 155 a-155 c, such as local correlator155 a-c described in relation to FIG. 1. The plurality of localcorrelators will each generally be referred to as local correlator 155or collectively referred to as local correlators 155. The localcorrelation sub-systems 220 receive correlated anomalous groups oftime-series data over the network 210 from the respective globalcorrelation sub-system 215. The local correlators 155 process thecorrelated anomalous groups of time-series data to generate detailedstatistical data and a detailed statistical report that is associatedwith each group of correlated anomalous data. The local correlationsub-systems 220 may transmit the detailed statistical reports over thenetwork 210 for processing by the reporting sub-system 225. Thereporting sub-system 225 includes a reporting module, such as reportingmodule 160 described in relation to FIG. 1.

As shown in FIG. 2, the anomaly detection system 205, the globalcorrelation sub-system 215, the local correlation sub-systems 225, andthe reporting sub-system 225 are configured on individual servers in adistributed server architecture 200. In some implementations, eachsystem and/or sub-system may be configured on a separate server. In someimplementations, individual systems and/or sub-systems may be combinedon one or more servers. In some implementations, the individual systemsand/or sub-systems may be implemented individually or combined on one ormore virtual machines. In some implementations, the individual systemsand/or sub-systems may be implemented individually or combined in one ormore containerized environments. The individual systems and/orsub-systems may be implemented in such a distributed architecture 200 toenable greater parallelization of the anomaly detection and correlationprocessing that is performed by the components, systems, and/orsub-systems. In this way, the architecture 200 may enable greaterscalability and increased processing capabilities than may be achievedin a non-distributed architecture. The distributed arrangement of thecomponents, systems, and/or sub-systems as shown in FIG. 2 may alsoallow the detection and correlation processing of anomalous time-seriesdata to occur at or near real-time execution speeds.

FIG. 3 illustrates an example method 300 for detecting and correlatinganomalous time-series data performed by the components of the anomalydetection and correlation system 110 shown in FIG. 1. The method 300includes receiving a plurality of time-series data (stage 310). Themethod further includes generating aligned time-series data (stage 320)and generating annotated time-series data (stage 330). The methodincludes outputting correlated anomalous groups of time-series data(stage 340) and generating a detailed statistical report for eachcorrelated anomalous group (stage 350). The method further includesoutputting an aggregated statistical report (stage 360).

At stage 310, the method 300 begins by the data collector 130 receivinga plurality of time-series data, such as the time-series data that isstored in the time-series data sources 105 shown in FIG. 1. Theplurality of received time-series data may include a plurality oftime-series data types, such as binary time-series data, categoricaltime-series data, and/or real-valued time-series data. The time-seriesdata may be associated with one or more network data streams that may bereceived from one or more external sources. The data collector 130 mayprocess the received time-series data and may condition or clean thedata for subsequent processing by the anomaly detection sub-system 135.

At stage 320, the data collector 130 temporally aligns the time-seriesdata and generates one or more sets of aligned time-series data. Themethod steps and processing details performed by the data collector 130on the time-series data received from the plurality of time-series datasources 105 will be described below in relation to FIG. 4.

At stage 330, the detectors 140 of the anomaly detection sub-system 135generate annotated time-series data. The anomaly detection sub-system135 receives the sets of aligned time series data generated by the datacollector 130 in stage 320 and the plurality of detectors 140 processthe received time-series data to detect anomalous time-stamped datapoints that may be present in each of the one or more sets of alignedtime-series data. The detectors 140 perform per-time-series anomalydetection to filter out irrelevant data. The detectors 140 may annotateanomalous time-stamped data points that are detected in the sets ofaligned time-series data and may generate one or more groups ofannotated time-series data. Each annotated group of time-series data mayinclude one or more individually annotated anomalous time-stamped datapoints that were found to be present in the plurality of time-stampeddata points included in each set of aligned time-stamped data. Themethod steps and processing details performed by the anomaly detectionsub-system 135 on the sets of aligned time-series data received from thedata collector 130 will be described below in relation to FIG. 5.

At stage 340, the anomaly correlation sub-system 145 outputs correlatedanomalous groups. The sets of annotated time-series data generated bythe detectors 140 of the anomaly detection sub-system 135 are receivedby the anomaly correlation sub-system 145 where the global correlator150 may process the sets of annotated time-series data to determine thestatistical correlation of the annotated time-stamped data identified instage 330. The global correlator 150 may divide the sets of annotatedtime-series data into smaller groups so that there is no or only limitedcross-group correlation across the groups. In this way, the globalcorrelator 150 may determine a number of correlated anomalous groups ofannotated time-series data within all of the one or more groups ofannotated time-series data received from the detectors 140. The globalcorrelator 150 may output the correlated anomalous groups. The methodsteps and processing details performed by the anomaly correlationsub-system 135 and its components therein on the sets of annotatedtime-series data received from the anomaly detection sub-system 135 willbe described below in relation to FIG. 6.

At stage 350, the local correlators 155 of the of the anomalycorrelation sub-system 145 generate detailed statistical reports foreach of the correlated anomalous groups. The local correlators 155receive the correlated anomalous groups output by the global correlator150 in stage 340 and process the received time-series data to generatespecific statistics for each group of correlated anomalous time-seriesdata. The statistical methods applied to each group may include but arenot limited to determining the Pearson correlation coefficient, theJaccard similarity coefficient, and/or the Bayes factors. The localcorrelators 155 may include the results of the applied statisticalmethods in a detailed statistical report that is associated with thecorrelated anomalous groups and the anomalies identified therein. Thelocal correlators 155 may generate the detailed statistical report forsubsequent processing. The method steps and processing details performedby the local correlators 155 on the correlated anomalous groups oftime-series data received from the global correlator 150 will bedescribed below in relation to FIG. 7.

At stage 360, the reporting module 160 outputs an aggregated statisticalreport. The reporting module 160 receives the detailed statisticalreports generated by the local correlators 155 in stage 350 andaggregates the detailed statistical report data for each correlatedanomalous group into an aggregated statistical report. The aggregatedstatistical report may be formatted such that the report ishuman-interpretable or readily interpreted by a human. The aggregatedstatistical report may include probability data, such as the probabilitythat a single network entity is associated with a network failure. Thereporting module 160 may output the aggregated statistical report. Insome implementations, the aggregated statistical report may be output tousers via one or more application programming interfaces (APIs). Themethod steps and processing details performed by the reporting module160 on the detailed statistical reports received from the localcorrelator 155 will be described below in relation to FIG. 7.

FIG. 4 illustrates an example method 400 for generating alignedtime-series data performed by the data collector 130 shown in FIG. 1.The method 400 describes the method steps associated with generatingaligned time-series data which was described earlier in relation tostage 320 of FIG. 3. The method 400 includes normalizing time-seriesdata (stage 410) and imputing missing values (stage 420). The methodalso includes time-stamp up-sampling or time-stamp down-sampling (stage430) and noise removal (stage 440). The method includes temporallyaligning time-series data (stage 450).

At stage 410, the method 400 begins by the data collector 130normalizing the time-series data that was received from the plurality oftime-series data sources 105. The data collector 130 may clean orcondition the received data for later processing to ensure more accuratemost accurate anomaly detection and correlation. As the data can beassociated with one or more network data streams that may be receivedfrom a variety of external sources, the data may be of an undeterminedquality. The data collector 130 may perform the following method stepsto enhance the quality of data so that subsequent anomaly detection andcorrelation can be performed in the most robust manner possible. Forexample, in stage 410 the data collector 130 may normalize the receivedtime-series data. Normalizing the time-series data rescales the datafrom its original range of values so that all values are within therange of 0 and 1.

At stage 420, the data collector 130 imputes missing values. The datacollector 130 may process the received time-series data and determinethat one or more values are missing. Missing data can have adverseeffects on the anomaly detection because the detectors 140 may falselyidentify a missing value as an anomalous data point. The result of thisfalse identification may be an over-estimation of the number ofanomalous data points present with the received time-series data. Thedata collector 130 may include logic, algorithms or other ways ofprocessing the received time-series data in order to identify and inputmissing values as appropriate based on the data type associated with thereceived time-series data.

At stage 430, the data collector 130 performs time-stamp up-samplingand/or time-stamp down-sampling. In up-sampling, the frequency of thetime-series data is increased. In down-sampling, the frequency of thetime-series data is decreased. For example, the received time-seriesdata may have been collected on an hourly basis. Up-sampling the hourlytime-series data to a basis of every 15 minutes would generate a new setof time-series data with extended values corresponding to the new timebasis (e.g., every 15 minutes). Time-stamp up-sampling may producemissing values that must be filled by interpolation or by inputtingmissing values as described in stage 420. Time-stamp down-sampling mayrequire careful selection of the statistical methods used to calculatenew aggregated time-series data points, when, for example, the basis ofthe time-series data is changed from microseconds to seconds.

At stage 440, the data collector 130 performs noise removal. The datacollector 130 may process the received time-series data to remove noisefrom the data using a variety of mathematical methods and/or algorithms.The method selected may depend on the data type of the time-series data,as well as the level of dimensionality of the time-series data. Forexample, noise may be removed in the received time-series data usingmedian, mean, or trimmed mean absolute deviations. In someimplementations, the noise removal may be performed using deconvolutiontechniques such as Weiner filtering, blind convolution techniques,exponential smoothing, outlier removal or substitution, as well asindependent component analysis techniques.

At stage 450, the data collector temporally aligns time-series data. Thedata collector 130 may process the received time-series data to alignthe data temporally or in the context of time. When processing largevolumes of time-series data, it is important to recognize that the datamay include variability affecting the time scale on which the data wasmeasured. For example, the time axes may have been shifted, compressed,or even expanded in complex, non-linear ways. In some cases, the scaleof the measured time-series data can be inconsistent between sets of thesame data. As a result, it is prudent to temporally align thetime-series data. The data collector 130 may apply logic or algorithmssuch as the dynamic time warping algorithm used to measure similaritybetween two temporal sequences in order to align the time-series data ina temporal manner. The data collector 130 outputs one or more sets oftemporally aligned time-series data to the anomaly detection sub-system135.

FIG. 5 illustrates an example method 500 for generating annotatedtime-series data performed by the detectors 140 that may be configuredwithin the anomaly detection sub-system 135 shown in FIG. 1. The method500 describes the method steps associated with generating alignedtime-series data which was described earlier in relation to stage 330 ofFIG. 3. The method 500 includes selecting a virtual interface based onthe data type of the aligned time-series data (stage 510). The methodalso includes discretizing the aligned time-series data (stage 520). Themethod includes processing binary data types (stage 530), processingreal-value data types (stage 540), and processing categorical data types(stage 550). The method also includes annotating anomalous time-stampeddata points (stage 560).

At stage 510, the method 500 begins by the anomaly detection sub-system135 receiving the sets of aligned time-series data generated by the datacollector 130. The anomaly detection sub-system 135 may include aplurality of detectors 140. Each detector 140, such as detectors 140a-140 c shown in FIG. 1, may implement a different virtual interface forperforming anomaly detection. The different implementations may be basedon or correspond to the data types of the time-series data that wasreceived from the time-series data sources 105. For example, detector140 a may be configured to detect anomalies within binary time-seriesdata, such as time-series data that is received from the binarytime-series data source 105 b. As time-series data is received from thedata collector 130, the anomaly detection sub-system 135 may select theappropriate virtual interface that is configured on a particulardetector 140 and upon selection, forward the aligned time-series data tothe selected detector 140 for anomaly detection. Each detector 140 mayimplement different processing techniques that correspond to the datatype of the received time-series data.

At stage 520, the anomaly detection sub-system 135 discretizes thealigned time-series data. The anomaly detection sub-system 135 maydiscretize the aligned time-series data in order to convert the alignedtime-series data into a smaller number of finite values. Discretizationtypically involves the process of transferring continuous functions,models, equations, and/or data (e.g., time-series data) into discretecounterparts. Discretization further enables the data to be moresuitable for numerical evaluation and implementation on computingdevices. As used in the method performed by the anomaly detectionsub-system 135, discretizing the aligned time-series data has the effectof emulating network failure data more accurately. For example, as aresult of discretization, the original time-series data becomes sparse,consisting mostly of zeroes and the occasional non-zero integer valuewhich may correspond to an anomaly. A variety of discretizationpre-processing steps may be used.

At stage 530, one of the detectors 140 processes binary data types.Binary data types may include types of data for which the data valuesmay only represent a “0” or a “1” for more than a certain number ofsamples. Upon determining the data type of the data included in the setof annotated time-series data received from the data collector 130, theanomaly detection sub-system 135 identifies the appropriate detector 140that is configured to process the received time-series data type anddetect anomalies. For example, detector 140 a may be configured toprocess binary time-series data types and detect anomalies. The detector140 a may detect and identify binary time-series data values as ananomaly if the data value is “1”. If the data value is “0”, the detector140 a may identify the binary time-series data value as not anomalous.Upon detecting anomalous data values in the binary time-series data, thedetector 140 a may annotate the binary time-stamped data values asanomalous.

At stage 540, one of the detectors 140 processes real-value data types.Real-value data types may include types of data for which the datavalues may be any numerical value, such as “1.5”, “25.6”, or “89”. Upondetermining that the data type of the data included in the set ofannotated time-series data includes real-value data types, the anomalydetection sub-system 135 identifies the appropriate detector 140 that isconfigured to process real-value time-series data. The detector 140configured to process real-value data types may apply specificprocessing to the real-value time-series data. For example, whenprocessing latency histogram values, where the value may represent areal-value data type that is associated with the latency between twonetwork entities (e.g., measured in milliseconds), the detector 140 thathas been identified to process real-value time-series data types mayfirst convert the latency histogram data into a cumulative distributionfunction (CDF) curves representing the real-value latency data. The CDFcurves may then be normalized and the detector 140 may then determinethe differences in the area under the curve. Upon detecting anomalousdata values in the real-value time-series data that are outside the areaunder the curve, the identified detector 140 may annotate thosereal-value time-stamped data values as anomalous.

At stage 550, one of the detectors 140 processes categorical data types.Categorical data types may include types of data for which the datavalues may be one of multiple selections, such as a categorical datatype that identifies network entity ownership. There may be more thantwo possible network owners associated with a particular network entity.The ownership of the network entity may change over time. Upondetermining that the data type of the data includes in the set ofannotated time-series data includes categorical data types, the anomalydetection sub-system 135 identifies the appropriate detector 140 that isconfigured to process categorical time-series data. The identifieddetector 140 may apply specific processing to the categoricaltime-series data. For example, a change in the categorical data value ora value spike at a specific time-stamp may indicate an anomalous datapoint. In some implementations, thresholds can be learned fromhistorical data and used to identify anomalies for future evaluations ofdata represented as categorical time-series data types. Upon detectinganomalous data values in the categorical time-series data, theidentified detector 140 may annotate those categorical time-stamped datavalues as anomalous.

At stage 560, the detectors 140 annotate anomalous time-stamped datapoints. As described above in relation to the data-type-specificprocessing that is performed by the detectors 140, anomaloustime-stamped data points may be annotated to identify the data points asan anomaly. The annotation may be a unique identifier that is applied toanomalous data points. In some implementations, the unique identifiermay be based on the data type of the anomalous data point in order todistinguish the resulting groups of anomalous data of one data-type fromthe anomalous groups identified for a different data-type.

FIG. 6 illustrates an example method 600 for correlating anomalousgroups of time-series data performed by the global correlator 150 thatmay be configured within the anomaly correlation sub-system 145 shown inFIG. 1. The method 600 describes the method steps associated withoutputting correlated anomalous groups which was described earlier inrelation to stage 340 of FIG. 3. The method 600 includes determining thenumber of anomalous groups of annotated time-series data within all ofthe groups of annotated time-series data (stage 610). The methodincludes determining the probability that each anomalous group ofannotated time-series data belongs to one of the groups of annotatedtime-series data using a generative statistical model (stage 620). Themethod also includes determining whether or not the annotatedtime-series groups are statistically correlated (stage 630). The methodincludes, responsive to determining that the annotated time-seriesgroups are statistically correlated, grouping the statisticallycorrelated anomalous groups (stage 640) and outputting the correlatedanomalous groups (stage 650). The method also includes, responsive todetermining that the annotated time-series groups are not statisticallycorrelated, storing the un-correlated groups (stage 660).

At stage 610, the global correlator 150 receives the one or more groupsof annotated time-series data generated by the local detectors 140 anddetermines the number of anomalous groups of annotated time-series datawithin all of the groups of annotated time-series data. In this way, thelikelihood of cross-group correlation and inaccurate anomaly correlationmay be reduced or avoided. In addition, by dividing the groups ofannotated time-series data into smaller groups, the groups may beprocessed in parallel, for example in a distributed architecture similarto that shown in FIG. 2, configured with multiple anomaly correlationsub-systems 215. The global correlator 150 may be configured to utilizea locality sensitive hashing algorithm to detect the number of anomalousgroups or potentially anomalous groups across all of the annotatedtime-series groups received from the detectors 140. Locality sensitivehashing (LSH) serves to reduce the dimensionality of high-dimensionaldata, such as time-series data. LSH hashes the inputted annotated groupsof time-series data so that similarly annotated time-stamps in eachgroup may be mapped or grouped as an anomalous group of annotatedtime-series data.

At stage 620, the global correlator 150 determines the probability thateach anomalous group of annotated time-series data belongs to one of thegroups of annotated time-series data using a generative statisticalmodel. The groups of anomalous annotated time-series data which includereal-values data types may be transformed into binary or categoricaldata types by calculating the mean and standard deviations for eachgroup of time-series data. The new value will be how many standarddeviations the old value is from the mean. With the number of groups ofanomalous annotated time-series data now known, the number of groups maybe used as an input parameter to the generative statistical model inorder to determine the probability that each anomalous group ofannotated time-series data belongs to one of the groups of annotatedtime series data.

Generative statistical models are models used for generating values thatmay be associated with a phenomenon, such as anomalous time-series datathat is associated with a network failure event. The generativestatistical models generate values associated with phenomenon that maybe observed as well as phenomenon that may be hidden. Generativestatistical models are typically probabilistic and specify a jointprobability distribution over the observed and hidden phenomenon values.Examples of generative statistical models include Gaussian mixturemodels, hidden Markov models, naïve Bayes models and latent Dirichletallocation models. Latent dirichlet allocation (LDA) modeling is anatural language processing technique that can infer latent topics, orgroupings of words, that may be likely to occur in a set of documents.LDA may also be used for anomaly correlation by considering the discretetime-stamps data points of individual time-series data as “documents”and the network entities that failed within each particular discretetime-stamp data point as the corresponding document “words”. Bydetermining and inputting the number of anomalous annotated groups oftime-series data as the number of observed “topics”, the LDA model mayoutput a distribution of probabilities of failing network entities pertopic, where the entities associated with higher probabilities may bemost likely to fail simultaneously over the time period captured by thecollection of individual time-series data that was input to the model.In this way, groups of correlated failing network entities may bedetermined based on temporal failure patterns without performingexhaustive pairwise comparisons of individual time-series data. This ispossible because the LDA model assumes that the “documents” or discretetime-stamps data points of individual time-series data will be sparseand include relatively few failures (or detected anomalies) compared tothe time-series data that is associated with the total number of networkentities.

In addition, LDA models may be trained to explain network failure eventsthat may be associated with independent latent factors. Each factor mayconsist of a set of links connecting one or more network entities thattend to historically fail together. In this mixed-membership model, alink failure can be attributed to different factors at differenttime-stamps. The LDA model may learn sets of independent and sparsefactors, for example each factor may be mapped to a small number offailure patters that occur simultaneously. The LDA model may also allowuse of domain knowledge. For example, the physical single points ofnetwork failures may be modeled explicitly in the LDA training process.In this example, the link-to-factor assignment may be fixed and only thefailure probability may be learned from the model. The LDA modeltraining process may be implemented using a feedback loop between theanomaly correlation sub-system 145 and the anomaly detection sub-system135, as shown in FIG. 1 as a bi-directional arrow between the twosub-systems.

At stage 630, the method includes determining whether or not the groupsof anomalous time-series data are statistically correlated. The globaldetector 150 may compare the probabilities generated by the LDA modeland statistically correlate one or more anomalous groups based on thedetermination that one or more groups include one or more statisticallycorrelated anomalous time-stamped data points. In some implementationsthe statistical correlation may be based on one or more probabilitiesexceeding a pre-determined threshold. For example, the global correlator150 may determine that one or more groups of anomalous time-series datamay be statistically correlated based on the output distribution ofprobabilities for one or more groups exceeding a particular thresholdvalue.

At stage 640, responsive to determining that one or more groups ofanomalous time-series data are statistically correlated, the globalcorrelator 150 may group the statistically correlated anomalous groups.For example, the global correlator 150 may group correlated anomalousgroups of time-series data based on two or more of the correlatedanomalous groups based on the two or more groups including the one ormore shared network entities that have failed. In some implementations,the global correlator 150 may group correlated anomalous groups based onthe two or more correlated groups including similar failureprobabilities as determined by the LDA model in stage 620. In someimplementations, the global correlator 150 may group correlatedanomalous groups based on the two or more correlated groups includingfailure probabilities that are within a range of pre-determined values.

At stage 650, the global correlator 150 outputs correlated anomalousgroups. The global correlator 150 may output the correlated anomalousgroups to the plurality of local correlators 155 as shown in FIG. 1 or2.

At stage 660, responsive to determining that one or more groups ofanomalous time-series data are not statistically correlated, the globalcorrelator 150 may store the statistically un-correlated groups. Groupsare considered statistically un-correlated if the global correlator 150has determined the groups do not include correlated anomalous time-stampdata, or the correlation between the data in the groups is below apre-selected correlation threshold. In such situations, the globalcorrelator 150 may, for example, store the statistically un-correlatedgroups in memory or a database. In some implementations, the globalcorrelator 150 may store the statistically un-correlated groups for usein training the LDA model.

FIG. 7 is an example functional block diagram for generating detailedstatistical reports for each correlated anomalous group and outputtingan aggregated statistical report. The diagram 700 includes similarcomponents as described in relation to FIG. 1, however for clarity, thedata collector 130 and the anomaly detection subsystem 135 have beenremoved from the anomaly detection and correlation system 110 in orderto describe the processing performed by the local correlators 155 andthe reporting module 160 in more detail.

As shown in FIG. 7, the anomaly correlation sub-system 145 includes aglobal correlator 150 and a plurality of correlated anomalous groups705, e.g., correlated anomalous groups 1-3. The anomaly correlationsub-system 145 also includes a local correlator 155 a. The localcorrelator 155 a includes a plurality of calculators such as the Pearsoncorrelation coefficient calculator 710, the Jaccard similaritycoefficient calculator 715, and the Bayes factor calculator 720. Thelocal correlators 155, such as local correlator 155 a, may also beconfigured to include a variety of other calculators as shown bycalculator N 725. The anomaly detection and correlation system 110includes a plurality of detailed statistical reports 730 and a reportingmodule 160. The architecture 700 includes an aggregated statisticalreport 735, a computing device 740 and a plurality of APIs 745.

As shown in FIG. 7, the anomaly correlation sub-system 145 includes aglobal correlator 150. The global correlator 150 may determine thenumber of anomalous groups and outputs one or more correlated anomalousgroups 705. The global correlator outputs the correlated anomalousgroups as described in relation to method step 340 shown in FIG. 3. Theglobal correlator 150 outputs the correlated anomalous groups 705 to thelocal correlator 155 a.

As further shown in FIG. 7, the anomaly correlation sub-system 145includes a local correlator 155, such as local correlator 155 a. Thelocal correlator 155 a includes a plurality of calculators that may beconfigured to generate specific statistical data for each group ofcorrelated anomalous time-series data received from the globalcorrelator 150. The local correlator 155 a includes a Pearsoncorrelation coefficient calculator 710, a Jaccard similarity coefficientcalculator 715, and a Bayes factor calculator 720. The local correlators155, such as the local correlator 155 a, may also include any number ofcalculators, shown as calculator N 725, that are appropriate forproviding statistics related to a received group of correlated anomaloustime-series data 705.

The Pearson correlation coefficient (PCC) calculator 710 may be used togenerate a measure of the linear correlation between two variables. ThePearson correlation coefficient calculator 710 may generate a value thatis between +1 and −1, where +1 is indicative of a total positive linearcorrelation, 0 is indicative of no linear correlation, and −1 isindicative of a total negative linear correlation. The local correlator155 a may apply the Pearson correlation coefficient calculator 710 toone or more correlated anomalous groups 705 and determine the Pearsoncorrelation coefficient between the correlated anomalous time-stampeddata points within each correlated anomalous groups 705.

As further shown in FIG. 7, the local correlator 155 a includes aJaccard similarity coefficient calculator 715. The Jaccard similaritycoefficient calculator 715 may generate a statistic used for comparingthe similarity and diversity of input sample sets. The Jaccardsimilarity coefficient measures similarities between finite sample setsand is defined as the size of the intersection divided by the size ofthe union of the sample sets. The Jaccard similarity coefficient may berepresented as a percentage identifying the degree of similarity betweentwo sets of data. For example, a Jaccard similarity coefficient of 100%indicates that two sets of data share all of the same members, while aJaccard similarity coefficient of 0% indicates that the two sets shareno members. A Jaccard similarity coefficient of 50% indicates that thetwo sets share half of the members. In some implementations, the localcorrelator 155 a may apply the Jaccard correlation coefficientcalculator 715 to the correlated anomalous groups 705 received from theglobal correlator 150 and determine the Jaccard correlation coefficientsbetween the correlated anomalous time-stamped data points within eachcorrelated anomalous groups 705.

As shown in FIG. 7, the local correlator 155 a includes a Bayes factorcalculator 720. The Bayes factor calculator 720 may generate a Bayesfactor that represents a ratio of the likelihood probability of twocompeting hypotheses, usually a null hypothesis and an alternativehypothesis. The Bayes factor is a way of quantifying support for oneparticular hypothesis model over another in order to determine whichparticular hypothesis model is true. Various scales have been proposedin literature to assist interpreting the calculated Bayes factor values.For example, Bayes factors that range from 1-3 indicate the strength ofone particular hypothesis over a second hypothesis is barely worthmentioning, Bayes factors that range between 3-20 indicate positiveevidence that one particular hypothesis is stronger than a secondhypothesis, while Bayes factors that range between 20-150 indicatestrong evidence that one particular hypothesis is stronger than a secondhypothesis. In some implementations, the local correlator 155 a mayapply the Bayes factor calculator 720 to the correlated anomalous groups705 to determine that the correlated anomalous time-stamped data pointswithin each group are anomalous when compared to other correlatedanomalous time-stamped data points within the same group.

As further shown in FIG. 7, the local correlators 155, such as localcorrelator 155 a, output one or more detailed statistical reports 730 asdescribed in relation to method step 350 shown in FIG. 3. The detailedstatistical reports 730 generated by the local correlator 155 a aresubsequently processed by the reporting module 160. The reporting module160 may collect or receive the detailed statistical reports 730generated for each correlated anomalous group 705 and output anaggregated statistical report 735 for one or more of the correlatedanomalous groups. The reporting module 160 may output the aggregatedstatistical report 735 as described in relation to method step 360 shownin FIG. 3.

As shown in FIG. 7, the aggregated statistical report 735 may includesummarized statistical data for one or more correlated anomalous groups705. The aggregated statistical report 735 may be formatted in a mannerthat is easily interpreted by humans. The aggregated statistical report735 may include the probability a single network entity may fail, aswell as the probabilities a group of network entities may fail. Forexample, as shown in FIG. 7, the aggregated statistical report 735indicates that switch X3A has a 0.75 (or 75%) probability of failingbased on the detected anomalies which were correlated in regard to linkconnectivity data associated with that particular switch. Similarly, thegroup of individual switches Y1C, Y2C, Y3C, Y4C, and Y5C (shown asY1C-Y5C) have been identified to have a 0.60 (or 60%) probability offailing based on the detection anomalies which were correlated in regardlink connectivity data associated with this group of individualswitches.

As further shown in FIG. 7, a computing device, such as computing device740 may interact with the anomaly detection and correlation system 110via one or more APIs 745 (e.g., APIs A-C). For example, a user ofcomputing device 740 may submit commands via one or more APIs 745 to theanomaly detection and correlation system 110. The API 745 may specifycomputer-readable executable instructions for the reporting module 160that may be configured in the anomaly detection and correlation system110 to output the aggregated statistical report 735 to the computingdevice 740.

FIG. 8 is a block diagram 800 illustrating an example computer system810 with which the time-series data sources 105, the anomaly detectionand correlation system 110 including any components therein of FIG. 1,and the computing device 740 of FIG. 7 can be implemented. In certainaspects, the computer system 810 may be implemented using hardware or acombination of software and hardware, either in a dedicated server, orintegrated into another entity, or distributed across multiple entities.

In broad overview, the computing system 810 includes at least oneprocessor 850 for performing actions in accordance with instructions andone or more memory devices 870 or 875 for storing instructions and data.The illustrated example computing system 810 includes one or moreprocessors 850 in communication, via a bus 815, with at least onenetwork interface driver controller 820 with one or more networkinterface cards 822 connecting to one or more network devices 824,memory 870, and any other devices 880, e.g., an I/O interface. Thenetwork interface card 822 may have one or more network interface driverports to communicate with the connected devices or components.Generally, a processor 850 executes instructions received from memory.The processor 850 illustrated incorporates, or is directly connected to,cache memory 875.

In more detail, the processor 850 may be any logic circuitry thatprocesses instructions, e.g., instructions fetched from the memory 870or cache 875. In many embodiments, the processor 850 is a microprocessorunit or special purpose processor. The computing device 810 may be basedon any processor, or set of processors, capable of operating asdescribed herein. The processor 850 may be a single core or multi-coreprocessor. The processor 850 may be multiple processors. In someimplementations, the processor 850 can be configured to runmulti-threaded operations. In some implementations, the processor 850may host one or more virtual machines or containers, along with ahypervisor or container manager for managing the operation of thevirtual machines or containers. In such implementations, the methodsshown and described in FIGS. 3-7 can be implemented within thevirtualized or containerized environments provided on the processor 850.

The memory 870 may be any device suitable for storing computer readabledata. The memory 870 may be a device with fixed storage or a device forreading removable storage media. Examples include all forms ofnon-volatile memory, media and memory devices, semiconductor memorydevices (e.g., EPROM, EEPROM, SDRAM, and flash memory devices), magneticdisks, magneto optical disks, and optical discs (e.g., CD ROM, DVD-ROM,and Blu-ray® discs). A computing system 810 may have any number ofmemory devices 870. In some implementations, the memory 870 supportsvirtualized or containerized memory accessible by virtual machine orcontainer execution environments provided by the computing system 810.

The cache memory 875 is generally a form of computer memory placed inclose proximity to the processor 850 for fast read times. In someimplementations, the cache memory 875 is part of, or on the same chipas, the processor 850. In some implementations, there are multiplelevels of cache 875, e.g., L2 and L3 cache layers.

The network interface driver controller 820 manages data exchanges viathe network interface driver 822 (also referred to as network interfacedriver ports). The network interface driver controller 820 handles thephysical and data link layers of the OSI model for networkcommunication. In some implementations, some of the network interfacedriver controller's tasks are handled by the processor 850. In someimplementations, the network interface driver controller 820 is part ofthe processor 850. In some implementations, a computing system 810 hasmultiple network interface driver controllers 820. The network interfacedriver ports configured in the network interface card 822 are connectionpoints for physical network links. In some implementations, the networkinterface controller 820 supports wireless network connections and aninterface port associated with the network interface card 822 is awireless receiver/transmitter. Generally, a computing device 810exchanges data with other network devices 824 via physical or wirelesslinks that interface with network interface driver ports configured inthe network interface card 822. In some implementations, the networkinterface controller 820 implements a network protocol such as Ethernet.

The other network devices 824 are connected to the computing device 810via a network interface driver port included in the network interfacecard 822. The other network devices 824 may be peer computing devices,network devices, or any other computing device with networkfunctionality. For example, a first network device 824 may be a networkdevice such as a hub, a bridge, a switch, or a router, connecting thecomputing device 810 to a data network such as the Internet or network210 shown in FIG. 2.

The other devices 880 may include an I/O interface, external serialdevice ports, and any additional co-processors. For example, a computingsystem 810 may include an interface (e.g., a universal serial bus (USB)interface) for connecting input devices (e.g., a keyboard, microphone,mouse, or other pointing device), output devices (e.g., video display,speaker, or printer), or additional memory devices (e.g., portable flashdrive or external media drive). In some implementations, a computingdevice 800 includes an additional device 880 such as a coprocessor,e.g., a math co-processor can assist the processor 850 with highprecision or complex calculations.

Implementations of the subject matter and the operations described inthis specification can be implemented in digital electronic circuitry,or in computer software embodied on a tangible medium, firmware, orhardware, including the structures disclosed in this specification andtheir structural equivalents, or in combinations of one or more of them.Implementations of the subject matter described in this specificationcan be implemented as one or more computer programs embodied on atangible medium, i.e., one or more modules of computer programinstructions, encoded on one or more computer storage media forexecution by, or to control the operation of, a data processingapparatus. A computer storage medium can be, or be included in, acomputer-readable storage device, a computer-readable storage substrate,a random or serial access memory array or device, or a combination ofone or more of them. The computer storage medium can also be, or beincluded in, one or more separate components or media (e.g., multipleCDs, disks, or other storage devices). The computer storage medium maybe tangible and non-transitory.

The operations described in this specification can be implemented asoperations performed by a data processing apparatus on data stored onone or more computer-readable storage devices or received from othersources. The operations may be executed within the native environment ofthe data processing apparatus or within one or more virtual machines orcontainers hosted by the data processing apparatus.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages, and it can be deployed in any form, including as astand-alone program or as a module, component, subroutine, object, orother unit suitable for use in a computing environment. A computerprogram may, but need not, correspond to a file in a file system. Aprogram can be stored in a portion of a file that holds other programsor data (e.g., one or more scripts stored in a markup languagedocument), in a single file dedicated to the program in question, or inmultiple coordinated files (e.g., files that store one or more modules,sub programs, or portions of code). A computer program can be deployedto be executed on one computer or on multiple computers or one or morevirtual machines or containers that are located at one site ordistributed across multiple sites and interconnected by a communicationnetwork. Examples of communication networks include a local area network(“LAN”) and a wide area network (“WAN”), an inter-network (e.g., theInternet), and peer-to-peer networks (e.g., ad hoc peer-to-peernetworks).

The processes and logic flows described in this specification can beperformed by one or more programmable processors executing one or morecomputer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinventions or of what may be claimed, but rather as descriptions offeatures specific to particular implementations of particularinventions. Certain features that are described in this specification inthe context of separate implementations can also be implemented incombination in a single implementation. Conversely, various featuresthat are described in the context of a single implementation can also beimplemented in multiple implementations separately or in any suitablesub-combination. Moreover, although features may be described above asacting in certain combinations and even initially claimed as such, oneor more features from a claimed combination can in some cases be excisedfrom the combination, and the claimed combination may be directed to asub-combination or variation of a sub-combination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the implementations described above should not beunderstood as requiring such separation in all implementations, and itshould be understood that the described program components and systemscan generally be integrated together in a single software product orpackaged into multiple software products.

References to “or” may be construed as inclusive so that any termsdescribed using “or” may indicate any of a single, more than one, andall of the described terms. The labels “first,” “second,” “third,” andso forth are not necessarily meant to indicate an ordering and aregenerally used merely to distinguish between like or similar items orelements.

Various modifications to the implementations described in thisdisclosure may be readily apparent to those skilled in the art, and thegeneric principles defined herein may be applied to otherimplementations without departing from the spirit or scope of thisdisclosure. Thus, the claims are not intended to be limited to theimplementations shown herein, but are to be accorded the widest scopeconsistent with this disclosure, the principles and the novel featuresdisclosed herein.

What is claimed is:
 1. A method for detecting and correlating anomaloustime-series data, the method comprising: detecting anomaloustime-stamped data points in each of one or more sets of alignedtime-series data; annotating each of the anomalous time-stamped datapoints; generating, based on the annotated time-stamped data points, oneor more groups of annotated time-series data; determining, based on theannotated time-series data, anomalous groups of annotated time-seriesdata within the one or more groups of annotated time-series data;determining, for each anomalous group of annotated time-series data, aprobability that the anomalous group belongs to at least one of the oneor more groups of annotated time-series data; and determining, based onthe determined probabilities, one or more correlated anomalous groupswithin the anomalous groups.
 2. The method of claim 1, wherein detectingthe anomalous time-stamped data points in each of the one or more setsof aligned time-series data is performed using one or more virtualinterfaces, wherein the one or more virtual interfaces are determinedbased on a data type of each of the one or more sets of the alignedtime-series data.
 3. The method of claim 2, wherein the one or more ofvirtual interfaces may detect the anomalous time-stamped data points inparallel.
 4. The method of claim 1, wherein detecting the anomaloustime-stamped data points includes discretizing each of the one or moresets of aligned time-series data.
 5. The method of claim 1, whereindetermining the anomalous groups within the one or more groups ofannotated sets of time-series data is performed using a localitysensitive hashing algorithm.
 6. The method of claim 1, whereindetermining the probability that the anomalous groups belongs to atleast one of the one or more groups of annotated time-series data anddetermining the one or more correlated anomalous groups is performed inparallel.
 7. The method of claim 1, further comprising: generating adetailed statistical report for each of the one or more correlatedanomalous groups; aggregating the detailed statistical reports for eachof the one or more correlated anomalous groups; and outputting theaggregated statistical report.
 8. A system for detecting and correlatinganomalous time-series data, the system comprising: a memory storing oneor more generative statistical models; and one or more processorscoupled to the memory, the one or more processors configured to: detectanomalous time-stamped data points in each of one or more sets ofaligned time-series data; annotate each of the anomalous time-stampeddata points; generate, based on the annotated time-stamped data points,one or more groups of annotated time-series data; determine, based onthe annotated time-series data, anomalous groups of annotatedtime-series data within the one or more groups of annotated time-seriesdata; determine, for each anomalous group of annotated time-series data,a probability that the anomalous group belongs to at least one of theone or more groups of annotated time-series data; and determine, basedon the determined probabilities, one or more correlated anomalous groupswithin the anomalous groups.
 9. The system of claim 8, furthercomprising one or more virtual interfaces, wherein detecting anomaloustime-stamped data points in each of the one or more sets of alignedtime-series data is performed using the one or more virtual interfaces,wherein the one or more virtual interfaces are determined based on adata type of each of the one or more sets of the aligned time-seriesdata.
 10. The system of claim 9, wherein the one or more of virtualinterfaces may detect the anomalous time-stamped data points inparallel.
 11. The system of claim 8, wherein detecting anomaloustime-stamped data points includes discretizing, by the one or moreprocessors, each of the one or more sets of aligned time-series data.12. The system of claim 8, wherein determining the anomalous groupswithin the one or more groups of annotated sets of time-series data isperformed using a locality sensitive hashing algorithm.
 13. The systemof claim 8, wherein determining the probability that the anomalousgroups belongs to at least one of the one or more groups of annotatedtime-series data and determining the one or more correlated anomalousgroups is performed in parallel.
 14. The system of claim 8, wherein theone or more processors are further configured to: generate a detailedstatistical report for each of the one or more correlated anomalousgroup; aggregate the detailed statistical reports for each of the one ormore correlated anomalous group; and output the aggregated statisticalreport.
 15. A non-transitory computer readable storage medium storinginstructions executable by a processor for performing a methodcomprising: detecting anomalous time-stamped data points in each of oneor more sets of aligned time-series data; annotating each of theanomalous time-stamped data points; generating, based on the annotatedtime-stamped data points, one or more groups of annotated time-seriesdata; determining, based on the annotated time-series data, anomalousgroups of annotated time-series data within the one or more groups ofannotated time-series data; determining, for each anomalous group ofannotated time-series data, a probability that the anomalous groupbelongs to at least one of the one or more groups of annotatedtime-series data; and determining, based on the determinedprobabilities, one or more correlated anomalous groups within theanomalous groups.
 16. The non-transitory computer readable medium ofclaim 15, wherein detecting the anomalous time-stamped data points ineach of the one or more sets of aligned time-series data is performedusing one or more virtual interfaces, wherein the one or more virtualinterfaces are determined based on a data type of each of the one ormore sets of the aligned time-series data.
 17. The non-transitorycomputer readable medium of claim 16, wherein the one or more of virtualinterfaces may detect the anomalous time-stamped data points inparallel.
 18. The non-transitory computer readable medium of claim 15,wherein detecting anomalous time-stamped data points includesdiscretizing each of the one or more sets of aligned time-series data.19. The non-transitory computer readable medium of claim 15, whereindetermining the anomalous groups within the one or more groups ofannotated sets of time-series data is performed using a localitysensitive hashing algorithm.
 20. The non-transitory computer readablemedium of claim 15, wherein determining the probability that theanomalous groups belongs to at least one of the one or more groups ofannotated time-series data and determining the one or more correlatedanomalous groups is performed in parallel.